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Recent results on Choi's orthogonal Latin squares.
- Source :
- Journal of Algebra Combinatorics Discrete Structures & Applications; 2022, Vol. 9 Issue 1, p17-27, 11p
- Publication Year :
- 2022
-
Abstract
- Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler although this was less known. He introduced a pair of orthogonal Latin squares of order 9 in his book. Interestingly, his two orthogonal non-double-diagonal Latin squares produce a magic square of order 9, whose theoretical reason was not studied. There have been a few studies on Choi's Latin squares of order 9. The most recent one is Ko-Wei Lih's construction of Choi's Latin squares of order 9 based on the two 3 3 orthogonal Latin squares. In this paper, we give a new generalization of Choi's orthogonal Latin squares of order 9 to orthogonal Latin squares of size n2 using the Kronecker product including Lih's construction. We find a geometric description of Choi's orthogonal Latin squares of order 9 using the dihedral group D8. We also give a new way to construct magic squares from two orthogonal non-double-diagonal Latin squares, which explains why Choi's Latin squares produce a magic square of order 9. [ABSTRACT FROM AUTHOR]
- Subjects :
- MAGIC squares
KRONECKER products
LEAST squares
Subjects
Details
- Language :
- English
- ISSN :
- 2148838X
- Volume :
- 9
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Algebra Combinatorics Discrete Structures & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 155075932
- Full Text :
- https://doi.org/10.13069/jacodesmath.1056511